I suggest you submit an online contact form; and someone at Spotify should be able to disassociate the old account with facebook manually and if they're feeling extra nice, connect the new one to your facebook account for you as well.
If you get an automated reply; make sure to reply to it directly (even if it's from a no reply); and it will be sent to the Spotify staff.
If they just disconnect it, then you can connect your fb account to your Spotify account under Edit>preferences then press 'connect to facebook' under the social section.
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Do you have a dedicated Spotify account, or did you create your Spotify account using Facebook?
If you are logged into a Spotify account, you will have a Edit/Spotify > Preferences > Social Network > Connect/Disconnect from Facebook which you can use to change the Facebook account linked to that Spotify username.
If you log into Spotify using your Facebook email address and password, then it is not possible to change the Facebook account associated with that Spotify account. If you need a hand moving your playlists over to a new account, get in touch with the team here and they will be able to help you with that.